The present invention relates generally to fast training of equalizers in DMT systems, and more particularly to multi-tone (multi-carrier) systems and the fast training of pre-equalizers for high-speed communications over severely distorting and/or severely long channel lines/loops.
In the telecommunications industry, information is transmitted over imperfect communication lines such as copper wire, TV cables, fiber optics, twisted pair, and the like. Such transmissions are also made in imperfect conditions and environments. Generally, any and all communication channels, even wireless systems that transmit signals through air, have undesirable parasitic characteristics (e.g., interference, line resistance, line capacitance, signal reflection, etc.) and external influences (e.g., crosstalk from other communication sources). These parasitics and influences result in dispersion of a transmitted signal and the smearing of adjacent data values over one another in the time domain. Such a dispersion phenomenon, referred to as intersymbol interference (ISI), is illustrated in FIG. 1.
FIG. 1 depicts a communication line or communication channel 10. Inside the box representing the channel 10 is depicted a time domain impulse response 12 for a typical channel 10. Specifically, if the channel 10 were subject to a transmitted impulse input xcex4(t) of very short time duration (e.g., lasting for a time period of only one sample interval at a given sampling frequency ƒs) the distorted response 12 would result at the receiving end of the channel 10. Due to the undesired parasitics of the channel 10 and external interference, response 12 is a signal that is spread over xcexd sampling intervals where xcexd is greater than the one sample interval in which the transmit signal xcex4(t) was initially contained. In short, response 12 indicates that the energy produced at the end of the channel 10 in response to a short-time duration impulse at time 0 is a smeared and distorted response that spans v sampling intervals. Such dispersion of a signal is common in all communications channels under various conditions. Therefore, FIG. 1 illustrates that if even a single bit of data (a single binary one value) is communicated through the channel 10 from a transmit side to a receive side (using some modulation scheme), that the receive side will receive a widely time dispersed and distorted xe2x80x9cimagexe2x80x9d of that one transmitted binary one value.
FIG. 1 further illustrates the impact the response 12 has on communicated data when transmitting asymmetric digital subscriber line (ADSL) data symbols over the channel 10. In an ADSL system, data is sent in discrete packets containing many frequency-coded digital bits. Each of the frequency-coded packets is transmitted by the transceiver for a time duration of about 250 microseconds whereby each packet is modulated using either 32 carriers (upstream direction, i.e., from remote to central office (CO) side) or 256 carriers (downstream direction, i.e., from central office to remote side). The packets are transmitted serially in time, one after the other, in order to communicate larger blocks of related data, voice, video, sound, or other information between users. Each packet, also referred to as a symbol, is physically sent through the channel using a digital-to-analog converter at the transmit side and retrieved using an analog-to-digital converter at the receive end. Due to the impulse response 12 of FIG. 1, each 250 microsecond transmitted symbols 14a and 16a is distorted and/or smeared at the receiving end over a longer time period of time than the desired 250 microseconds duration. FIG. 1 illustrates the smeared receive symbols 14b and 16b that are provided at,the receive end of the channel 10.
In most cases, adjacent smeared symbols 14b and 16b will overlap each other in time thereby causing an intersymbol-interference (ISI) region 18 as shown in FIG. 1. The ISI region is a period of time where data from symbol 14b is distorting data from symbol 16b and vice versa. One solution to the ISI problem is to throw away all ISI-distorted data that lies, within the ISI region 18. Another solution is to spread the symbols 14a and 16a farther apart from each other in time by using a larger dormant time period between symbols at the transmit end. By transmitting fewer symbols close to each other, it is possible to eliminate or reduce the size of the ISI region 18 at the receive end. Both of these xe2x80x9csolutionsxe2x80x9d greatly reduce the available data transmission rate and may increase the bit-error rate (BER) of the receive signal. Neither, reduced data rate nor increased BER is desired by the industry.
Furthermore, some channel lines 10 are so adversely subject to parasitics that a single 250 microsecond ADSL symbol may be smeared in time to result in a receive symbol that spans a time duration of more than one symbol. When viewed another way, any one single ADSL symbol at the receive end may be experiencing interference from several other ADSL symbols. To add to the problem of data recovery and integrity, an ADSL channel that transmits 1 unit of initial power at a transmit end will easily attenuate that power to 10xe2x88x926 units of power or less by the time the signal reaches the receive end of the channel 10. The combination of ISI and signal attenuation makes ADSL data transmission and recovery complex.
One common way to reduce ISI is to place a hard-wired time domain equalizer (TEQ) 20 serially in-line with the channel 10. Such a TEQ-based system is shown in FIG. 2. The main objective of the time domain equalizer (TEQ) 20 of FIG. 2 is to reduce the channel dispersion and the resulting intersymbol interference (ISI) by shortening the channel impulse response in time (see response 12 of FIG. 1) before discarding data samples. In other words, the channel 10 is initially analyzed to find its impulse response, and the TEQ 20 is then hard-wired to fixed filter coefficients that create a near inverse of this impulse response. With this fixed length channel and fixed TEQ, the combination (convolution) of the channel impulse response and the response of the TEQ 20 nulls out a substantial portion of the ISI whereby only the actual symbol data survives intact from the transmit side to the receive side.
Generally, reduction of ISI is achieved in the prior art by cascading the channel 10 (having an impulse response h with xcexd samples) with a finite impulse response (FIR) filter w of length Nw, which is know as the TEQ filter 20, where Nw, is a finite positive integer representing a number of data samples. Herein, underlined variable names are used to represent the signals or filter taps in a vector notation. The FIR filter response w is hard-wired, in response to data received by proper signal analysis of the channel 10, such that the combination of h and w has a Target Impulse Response (TIR) 22 shown in FIG. 2. Note that the response 22 is shorter in time than the unfiltered response 12 of FIG. 1 (i.e., the samples xcexd over which the response 12 extends is greater than the number of samples Nb over which the response 22 extends). The desired TIR 20 is an FIR filter b of length Nb, where Nb of FIG. 2 is much smaller than the length xcexd of the channel impulse response h of FIG. 1 (where h is a design constraint due to parasitics and external interference). By adding the fixed TEQ 20 in FIG. 2, the adverse ISI of FIG. 2 is contained within a window of Nb samples where Nb less than  less than xcexd (see xcexd in FIG. 1) so that less ISI occurs and reduced discarding of data is required in order to effectively transmit the original data 14a and 16a to the receive end.
In discrete multi-tone (DMT) modulation, the ISI will generally occur over the cyclic prefix (CP) portion of the data (which is non-data overhead in the ADSL symbol/packet). Since the CP is non-data overhead in the system, the CP information may be readily discarded over the ISI interval of Ncp samples without performance degradation. If Nb is equal or smaller than Ncp when taking out the CP portion of the data, ISI of the symbol data is totally eliminated via the system of FIG. 2.
One limiting factor in the fixed TEQ filter approach is that most telecommunications applications do not involve coupling a transmitter or receiver to a fixed length communication channel for all time. In addition, even fixed length communication lines will vary in their impulse response over time due to external interference, thermal changes, etc. Therefore, instead of hardwiring a TEQ 20 to a fixed channel 10, the TEQ 20 of FIG. 2 may be designed to be configurable upon initiation of a training period over the channel 10. Once the fixed-time-period training phase is initiated, the TEQ 20 iteratively adapts the TEQ 20 over time in order to progressively reduce ISI over the fixed time training phase. A block diagram of a common time domain equalization (TEQ) training system that adapts itself during a training cycle is shown in FIG. 3.
In FIG. 3, a known training sequence x is transmitted through the channel IO (or channel h as denoted in FIG. 3) from the transmitter 24. The receiver 26 internally uses the same training sequence to train the TEQ filter w. Generally, the training sequence x is a known signal of finite time duration that is fixed by a specific telecommunications specification (e.g., the specifications for one or more of V.90, V.34, power modems, ADSL, ISDN, etc.) so that the training sequence is easy to implement in a repeatable manner by both the transmitter 24 and the receiver 26. The receiver 26 delays the provision of the training sequence x, via a delay circuit 30, so that the signals r and z within the receiver coincide in time at the inputs to the adder circuit 32. In other words, the delay xcex94 that is created by circuit 30 is equal to the physical delay in the channel 10. The target impulse response (TIR) filter 28 is a finite impulse response (FIR) filter b of length Nb. The filters w and b are also known as the feedforward and feedback filters, respectively. In operation, the coefficients of the TEQ filter w and TIR b are adaptively adjusted, by a process discussed below, to minimize the mean squared error |e|2, where the output e (error) is shown to the right of FIG. 3. The value e is the difference between the receive-side""s internally-used training signal z and the signal r received from the transmitter through the actual channel 10 and the TEQ 20. An error e of near zero means that the ISI has been reduced to Nb samples, which are finally discarded within the receiver 26.
The feedback iterative process used in FIG. 3 to iteratively generate the filter coefficients in TEQ 20 during the training period is referred to as a conventional least mean squares (LMS) approach. The basic objective of the LMS method is to recursively minimize the mean squared error |e(i)|2 using the output data sequence y(i) measured for each frame/symbol and instantaneous gradient estimates. This method, initially disclosed by Chow et al. U.S. Pat. No. 5,285,474, issued on Feb. 8, 1994, and entitled xe2x80x9cMethod for Equalizing a Multicarrier Signal in a Multicarrier Communication System,xe2x80x9d has some limitations as discussed below. The prior art LMS method commonly in use today is as follows:
1. Given the training sequence x, obtain the channel output y(1) (signal y at a time 1) and initialize w to some starting values.
2.
3. Start transmitting data on the channel with the TEQ active.
The above algorithm usually requires a large number of iterations (N.) in order to converge to an optimal set of TEQ coefficients when used for a typical wireline channel. In addition to being very slow, the LMS algorithm discussed above may end up with a large residual error or misadjustment (which is the difference between the minimum mean square error of the LMS algorithm and the minimum mean square error of the optimum theoretical solution) at the end of the finite training period. This nonoptimal result of the LMS algorithm is due to the fact that the training time period is set by standards and is not a sufficiently long enough period of time to allow a slow LMS method to converge to optimal TEQ coefficients. Since the algorithm indicated above is slow, it does not converge to an optimal TEQ setting in the allotted training time period for most telecommunications standards. Therefore, when using the above method, full data transmission rate is not achieved and the maximal allowable line length may need to be reduced due to the nonoptimal convergence of the prior art LMS algorithm of FIG. 3.
In addition to the above issues, an intrinsic numerical limitation of the above LMS method is the time domain windowing (projection [.]+n) operation of b and w. In fact, one of the authors of the LMS TEQ training algorithm has disclosed recently that their algorithm could lead to worse performance when increasing the number of iterations. In other words, the prior art LMS algorithm may actually diverge during training operations whereby use of the LMS-corrected TEQ is even worse than if the system had merely left the channel alone and subject to full parasitic effects. See Pal et al., xe2x80x9cA New Method of Channel Shortening with Applications to Discrete Multitone (DMT) Systems,xe2x80x9d Proc. of the IEEE International Conference on Communications, vol. 2, pp. 763-768, June 1998.
Therefore, a new convergence method is needed to more intelligently and effectively reduce or eliminate ISI whereby the algorithm quickly converges to an optimum LMS solution. The algorithm should allow one or more of: (1) more data to be sent per symbol or packet; (2) more reliable and/or simpler data recovery; (3) closer packing of symbols over time to improve transmission rate; (4) improved signal to noise (SJN) ratio; and/or (5) the use of longer channel line lengths. This new method of training a TEQ system should overcome one or more of the major weaknesses the conventional LMS TEQ training algorithm, which are: (1) lack of speedy convergence (or the necessity of longer training times in standards); (2) slower convergence or lack training time period) of convergence for long channel lengths; (3) potential for divergence from an optimal solution; and/or (4) failure to converge to an optimal solution within currently set standard training times whereby present telecommunication performance is degraded.